Big grains in the red rectangle?

We report VLA observations at 3.6 cm, 2 cm, and 1.3 cm of the Red Rectangle and H alpha spectroscopy of HD 44179, the central binary star in the nebulosity. Emission is detected at all three radio wavelengths, and the source is resolved at 2 cm and 1.3 cm. Convolved to the same beam, the radio spectrum of the inner 0.76 '' x 0.49 '' is characteristic of thermal emission from ionized gas which becomes optically thin near 2 cm. The diameter of the bulk of the ionized gas producing this radio emission is between 1.3 x 10(14) cm (similar to 10 AU) and 2 x 10(15) cm (similar to 100 AU); in this region we estimate that 10(6) cm(-3) less than or equal to n(e) less than or equal to 4 x 10(6) cm(-3). The H alpha profile has both a wide (200 km s(-1) full-width zero-intensity) plateau which is probably associated with a small circumstellar region (< 10(13) cm or similar to 1 AU) and a spike (FWHM approximate to 20 km s(-1)) which we suggest is produced in the extended ionized gas (greater than or equal to 10(14) cm) detected at radio wavelengths. We also detect low surface brightness radio emission at 2 cm and 1.3 cm, but not at 3.6 cm, that is extended well beyond 1 '' from the source. This extended radio emission has a spectral index between 1.3 cm and 3.6 cm greater than 3.2 and is therefore produced by grains. Our VLA data also indicate that the previously observed millimeter continuum flux cannot result from ionized gas and therefore is emitted by dust. Although uncertain, it is possible that the centimeter and millimeter wavelength continuum arise from the same dust, in which case there is probably little frequency variation in the emissivity of the dust between 1.3 cm and 0.13 cm. We propose that there is an orbiting, long-lived gravitationallly bound disk of dust grains with radii greater than or equal to 0.02 cm.